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Exploring Common Functions & Transformations

Study common functions like Constant, Absolute Value, Square Root, Quadratic, Cubing, Cube Root and their transformations. Learn about shifts and reflections, with guided practice and whiteboard problems.

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Exploring Common Functions & Transformations

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  1. A3 2.5a Common GraphsTransformations and Reflections Homework: p. 282-283 1-9, 17-25, 45-47, 67-73, 81-89 all odd!

  2. Introducing the Common Functions Constant Function: graph: domain: range: inc/dec/con: odd/even: Identity Function: graph: domain: range: inc/dec/con: odd/even:

  3. Introducing the Common Functions Absolute Value Function: graph: domain: range: inc/dec/con: odd/even: Square Root Function: graph: domain: range: inc/dec/con: odd/even:

  4. Introducing the Common Functions Standard Quadratic Function: graph: domain: range: inc/dec/con: odd/even: Standard Cubing Function: graph: domain: range: inc/dec/con: odd/even:

  5. Introducing the Common Functions And the last one… Cube Root Function: graph: domain: range: inc/dec/con: odd/even:

  6. Now transformations… Vertical Shifts: Horizontal Shifts: General Rule of Thumb: “outside the function” = vertical change “inside the function” = horizontal change

  7. Guided Practice Describe the transformations from f(x) to g(x). Graph the original and the transformed function.

  8. And now…Reflections! About the x-axis (outside the function) About the y-axis (inside the function) Managing the math: reflection about the x-axis : distribute the negative to every value in the function reflection about the y-axis : “run” a ( – x) through the function

  9. Guided Practice Describe the transformations on :

  10. Whiteboard Problems: 1. Describe the changes of to 2. Describe the changes of to

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